Problem: A bracket sequence is called regular if it is possible to obtain correct arithmetic expression by inserting characters + and 1 into this sequence. For example, sequences (())(), () and (()(())) are regular, while )(, (() and (()))( are not. Let's call a regular bracket sequence "RBS".

You are given a sequence s of n characters (, ), and/or ?. There is exactly one character ( and exactly one character ) in this sequence.

You have to replace every character ? with either ) or ( (different characters ? can be replaced with different brackets). You cannot reorder the characters, remove them, insert other characters, and each ? must be replaced.

Determine if it is possible to obtain an RBS after these replacements.

Input

The first line contains one integer t (1 ≤ t ≤ 1000) — the number of test cases.

Each test case consists of one line containing s (2 ≤ |s| ≤ 100) — a sequence of characters (, ), and/or ?. There is exactly one character ( and exactly one character ) in this sequence.

Output

For each test case, print YES if it is possible to obtain a regular bracket sequence, or NO otherwise}. 

You may print each letter in any case (for example, YES, Yes, yes, yEs will all be recognized as positive answer).

Example

Input


5
()
(?)
(??)
??()
)?(?


Output


YES
NO
YES
YES
NO

Note

In the first test case, the sequence is already an RBS.

In the third test case, you can obtain an RBS as follows: ()() or (()).

In the fourth test case, you can obtain an RBS as follows: ()().

Solution (in CPP):

Solution:

#include <bits/stdc++.h>
using namespace std;

template <typename A, typename B>
string to_string(pair<A, B> p);
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p);
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p);
string to_string(const string& s) {
    return '"' + s + '"';
}
string to_string(const char* s) {
    return to_string((string) s);
}
string to_string(bool b) {
    return (b ? "true" : "false");
}
string to_string(vector<bool> v) {
    bool first = true;
    string res = "{";
    for (int i = 0; i < static_cast<int>(v.size()); i++) {
        if (!first) {
            res += ", ";
        }
        first = false;
        res += to_string(v[i]);
    }
    res += "}";
    return res;
}
template <size_t N>
string to_string(bitset<N> v) {
    string res = "";
    for (size_t i = 0; i < N; i++) {
        res += static_cast<char>('0' + v[i]);
    }
    return res;
}
template <typename A>
string to_string(A v) {
    bool first = true;
    string res = "{";
    for (const auto &x : v) {
        if (!first) {
            res += ", ";
        }
        first = false;
        res += to_string(x);
    }
    res += "}";
    return res;
}
template <typename A, typename B>
string to_string(pair<A, B> p) {
    return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p) {
    return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " + to_string(get<2>(p)) + ")";
}
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p) {
    return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " + to_string(get<2>(p)) + ", " + to_string(get<3>(p)) + ")";
}
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
    cerr << " " << to_string(H);
    debug_out(T...);
}
template<typename T>
void read(T& val){
    cin >> val;
}
template<typename T>
void read(vector<T>& a){
    for(int i = 0; i < (int)a.size(); ++i){
      read(a[i]);
    }
}
template<typename Head, typename... Tail>
void read(Head& H, Tail&... T){
    read(H);
    read(T...);
}
#ifdef LOCAL
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif
#define endl '\n'
#define sz(x) (int)(x).size()
#define bits(x) __builtin_popcount(x)
#define vi vector<int> 
#define gcd(a, b) __gcd((a), (b))
template<typename T>
int64_t sum(vector<T> a){
    int64_t s = 0;
    for(int i = 0; i < (int) a.size(); ++i){
        s += a[i];
    }
    return s;
}
int query_number = 1;
void print_query(){
#ifdef LOCAL
    cout << "Query #" << query_number++ << ": ";
#endif
}
int test_case_number = 1;
void print_case(){
#ifdef LOCAL
    cout << "Case #" << test_case_number++ << ": ";
#endif
}

void solve(){
    string s; cin >> s;
    int n = sz(s);
    bool ok = 1;
    int bal = 0;
    int q = 0;
    for(int i = 0; i < n; ++i){
        char ch = s[i];
        if(ch == ')' && i == 0){
            ok = 0;
        }
        if(ch == '(' && i == n - 1){
            ok = 0;
        }
        if(ch == '?'){
            q ++;
        }
    }
    if(ok && q % 2 == 0) {
        cout << "YES" << endl;
    } else {
        cout << "NO" << endl;
    }
}

int32_t main(){
    ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
    // freopen(".in", "r", stdin); freopen(".out", "w", stdout);

    int t;
    cin >> t;
    while(t--){
        print_case();
        solve();
    }

}